TY - JOUR
T1 - Bulk and boundary S-matrices for the SU(N) chain
AU - Doikou, Anastasia
AU - Nepomechie, Rafael I.
N1 - Funding Information:
We are grateful to O. Alvarez and L. Mezincescu for valuable discussions. This work was supported in part by the National Science Foundation under Grant PHY-9507829.
PY - 1998/7/22
Y1 - 1998/7/22
N2 - We consider both closed and open integrable antiferromagnetic chains constructed with the SU(N)-invariant R-matrix. For the closed chain, we extend the analyses of Sutherland and Kulish - Reshetikhin by considering also complex "string" solutions of the Bethe ansatz equations. Such solutions are essential to describe general multiparticle excited states. We also explicitly determine the SU(N) quantum numbers of the states. In particular, the model has particle-like excitations in the fundamental representations [k] of SU(N), with k = 1,...,N - 1. We directly compute the complete two-particle S-matrices for the cases [1] ⊗ [1] and [1] ⊗ [N - 1]. For the open chain with diagonal boundary fields, we show that the transfer matrix has the symmetry SU(l) × SU(N - l) × U(l), as well as a new "duality" symmetry which maps l ↔ N - l. With the help of these symmetries, we compute by means of the Bethe ansatz for particles of types [1] and [N - 1] the corresponding boundary S-matrices.
AB - We consider both closed and open integrable antiferromagnetic chains constructed with the SU(N)-invariant R-matrix. For the closed chain, we extend the analyses of Sutherland and Kulish - Reshetikhin by considering also complex "string" solutions of the Bethe ansatz equations. Such solutions are essential to describe general multiparticle excited states. We also explicitly determine the SU(N) quantum numbers of the states. In particular, the model has particle-like excitations in the fundamental representations [k] of SU(N), with k = 1,...,N - 1. We directly compute the complete two-particle S-matrices for the cases [1] ⊗ [1] and [1] ⊗ [N - 1]. For the open chain with diagonal boundary fields, we show that the transfer matrix has the symmetry SU(l) × SU(N - l) × U(l), as well as a new "duality" symmetry which maps l ↔ N - l. With the help of these symmetries, we compute by means of the Bethe ansatz for particles of types [1] and [N - 1] the corresponding boundary S-matrices.
KW - Bethe ansatz
KW - Boundary S-matrix
KW - Boundary Yang-Baxter equation
KW - Duality
KW - Integrable spin chain
KW - SU(N) R-matrix
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U2 - 10.1016/S0550-3213(98)00239-9
DO - 10.1016/S0550-3213(98)00239-9
M3 - Article
AN - SCOPUS:0032558059
VL - 521
SP - 547
EP - 572
JO - Nuclear Physics B
JF - Nuclear Physics B
SN - 0550-3213
IS - 3
ER -